Types of customers and values.
TASK 2:
Activity #5
1. At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., the owner cannot directly price discriminate). The marginal cost of coffee is $0.10. The marginal cost of a banana is $0.40. Is bundling more profitable than selling separately? If so, what price should be charged for the bundle?
Students with Early Classes
Students without Early Classes
Coffee
$0.70
$0.60
Banana
$0.50
$1.00
2. Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator who chooses the best proposal (effectively giving one side or the other $2 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $400,000) who is effective at preparing the proposal in the best light. If neither hires lawyers or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win three-quarters of the time.
a. Diagram this simultaneous-move game.
b. What is the Nash equilibrium of the game?
c. Would the sides want to ban lawyers?
- Bundling vs. Separate Pricing
- Price Discrimination Challenge: Since the cafe owner can't distinguish between the two customer types, they can't charge different prices for coffee and bananas individually. "Students with Early Classes" value the bundle more (coffee: $0.70 + banana: $0.50 = $1.20) than "Students without Early Classes" (coffee: $0.60 + banana: $1.00 = $1.60). Separate pricing would lose out on this opportunity.
- Exploiting Surplus Value: By bundling, the cafe owner can create a package that captures some of the surplus value (willingness to pay above marginal cost) of "Students without Early Classes" for bananas. This increases overall profit.
- Minimum acceptable price for each customer type:
- "Students with Early Classes": combined marginal cost (coffee: $0.10 + banana: $0.40) = $0.50
- "Students without Early Classes": their minimum acceptable price for the bundle (to avoid buying separately) is likely lower than $1.60 (their separate value), but higher than $0.50 (combined marginal cost).
- Profit maximization: The price should be as high as possible while still attracting both customer types.
- Labor Negotiation Game
- Diagram:
| Labor (L) | Labor (N) | |
| Management (L) | (1, 1) | (0.75, 0.25) |
| Management (N) | (0.25, 0.75) | (0.5, 0.5) |
- Nash Equilibrium:
- For Management:
- If Labor hires a lawyer (L), Management should also hire one (L) to avoid losing most of the time (0.75 vs 0.25).
- If Labor doesn't hire a lawyer (N), Management is indifferent between hiring (0.5) or not (0.5). However, since hiring a lawyer is a cost, not hiring (N) might be a slightly better option.
- For Labor (similar logic):
- If Management hires a lawyer (L), Labor should also hire one (L) to avoid losing most of the time (0.25 vs 0.75).
- If Management doesn't hire a lawyer (N), Labor might be indifferent between hiring (0.75) or not (0.5). However, with the lawyer cost, not hiring (N) might be slightly better.
- Banning Lawyers?
- Cost savings: Each side would save $400,000 every year.
- Focus on negotiation: Without lawyers influencing the proposals, the focus might shift towards genuine negotiation and compromise.
- Information asymmetry: Lawyers might help prepare more compelling proposals, even if slightly slanted. Without them, one side might be at a disadvantage if less skilled at negotiation.
- Escalation of conflict: Without the "threat" of a lawyer-prepared proposal, negotiations might become more confrontational.